Labour has moved hastily to shut down speculation that it could withdraw support for Britain’s nuclear deterrent, after Jeremy Corbyn appeared to leave open the idea that renewing Trident could be left out of the party’s manifesto.

Labour issued a statement on Sunday saying: “The decision to renew Trident has been taken and Labour supports that. We also want Britain to do much more to pursue a proactive, multilateral disarmament strategy.”

It came three hours after the party’s leader had appeared to cast doubt on a future Labour government’s support for the nuclear deterrent system, and suggested he would think twice about backing a strike to kill the leader of Islamic State.

In an interview on the BBC1’s the Andrew Marr Show, Corbyn, who has been a longstanding campaigner against nuclear proliferation, said he did not believe it necessarily made the UK safer.

“I want us to achieve a nuclear-free world, to adhere to the nuclear non-proliferation treaty and take part in negotiations surrounding that,” he said, stressing an immediate need to take part in talks de-escalate nuclear tensions involving North Korea.

“The issue has to be that we want a secure and peaceful world,”Corbyn said. “You achieve that by promoting peace and also promoting security. Security comes from that process.”

It was the second time since Theresa May announced the snap general election last week that Labour has had to clarify statements made by the leader.

At Corbyn’s campaign launch event on Thursday, both he and the shadow chancellor, John McDonnell, appeared to refuse to rule out backing a referendum on the final Brexit deal. But the party later issued a statement saying a second referendum would not be in the manifesto.

Some Labour MPs who are facing a threat from the Liberal Democrats in heavily pro-remain seats would have liked to see a second referendum in the manifesto; but in leave seats, Labour fears it may be vulnerable to the charge of seeking to block Brexit.

The party’s current policy is to support Trident, backed by its party conference, but Labour split three ways when a vote on its renewal came to the House of Commons last July, with Corbyn himself voting against.

On Sunday, Corbyn said the policy would be reviewed by any Labour government. “We will have a strategic defence review immediately which would include all aspects of defence, but also make sure our armed forces are properly funded and play their part in peacekeeping around the world,” he said.

“We haven’t completed work on the manifesto. We are less than 100 hours into this election campaign. We are having this discussion within the Labour party.”

New prime ministers are asked to write “letters of last resort” on their first day in office, which are sealed and given to captains of the UK’s nuclear submarines in the event that the government is wiped out by a nuclear strike.

Pressed on whether, as prime minister, he would instruct a retaliation in his letter, Corbyn said: “I have made clear there would be no first use of it. I’ve made clear any use of nuclear weapons would be a disaster for the whole world.

“Nuclear weapons are not the solution to the world’s security issues. They are a disaster if ever used.”

Corbyn also made it clear that he did not back continued military intervention in Syria. He suggested he would suspend all UK strikes against Isis both there and in Iraq, and would call on Donald Trump to end strikes against the Syrian president, Bashar al-Assad.

“I will tell him I want to see a process that brings about an end to the conflict,” he said. “The only solution in Syria is going to be a political one. I would say to President Trump, it’s in no one’s interests for this war to continue.

“Let’s get the Geneva process going quickly, and in the meantime, no more strikes, have the UN investigation into the war crime of the use of chemical weapons in Syria and take it on from there.”

Corbyn also said he would be cautious about acting on military intelligence where he might be asked to authorise a drone strike on the Isis leader, Abu Bakr al-Baghdadi. “What is the objective? To have more strikes that would kill more possibly innocent people, or to get a political solution in Syria?” he said.

“Does this help to get a political solution? I think the leader of Isis not being around would be helpful, but I would also argue that the bombing campaign has killed a large number of civilians, many of them virtual prisoners of Isis.”

The home secretary, Amber Rudd, said the comments made it clear Corbyn would “refuse to strike against terrorists, dismantle our nuclear defences and fail to control our borders”.

Labour said after Corbyn’s interview it was Conservative spending cuts that put Britain’s security at risk. “Under them the army has shrunk to its smallest size since the Napoleonic wars,” a spokeswoman said. “Kneejerk decisions since 2010, like scrapping Nimrod, HMS Ark Royal and the Harrier jump jets, have weakened our defences and cost British taxpayers millions.

“The air force has been forced to rely on allies to track Russian subs off the UK coast, while the size of the navy’s fleet of frigates and destroyers has fallen to just 19. These kinds of cheap attacks simply show they are desperate to avoid scrutiny of their own record of failure.”

Corbyn also gave some further hints about a Labour government’s approach to the Brexit negotiations, but skirted a direct question on whether he would be in favour of keeping the EU’s free movement policy.

“I would insist on trade access and see what follows from there,” he said. “Free movement ends when we leave the EU. It’s an intrinsic part of membership. We then work out the system for people who come here for work and study, as well as British people allowed to go to work in Europe.”

Corbyn said a new immigration policy would have to be negotiated by necessity of the UK leaving the EU. “The first point is an economy that works for all. That means tariff-free access to the European market,” he said. “And then you work out an immigration policy that follows on from that. I would start from the point of view that I want to defend and maintain jobs in Britain.”

“The response I’ve had so far has been very positive. People need more time with their families. There’s so much insecurity in work, a public holiday celebrating the diversity of our nation is probably a good thing – don’t you think so?

“I’m out there, leading our party and very proud to do so. I will make that case to British people. We have had a huge increase in party membership in the past few days from people who see an opportunity of doing something different in Britain.”

This week’s revelation that a missile from a British submarine malfunctioned last year during a test flight off the coast of Florida has raised concerns about our ageing Trident missile system. Is it safe?